# Infinite Square Well with uniform probability density for a/4<x<3a/4

1. Oct 24, 2009

### zoso335

1. The problem statement, all variables and given/known data
The potential for an infinite square well is given by V=0 for 0<x<a and infinite elsewhere. Suppose a particle initially(t=0) has uniform probability density in the region a/4<x<3a/4 :
a.) Sketch the probability density
b.) Write an expression for the wavefunction as t=0
c.) Find the normalization constant
d.) What is the probability of finding the particle in the lowest eigenstate of the well?
e.) What is the probability of finding the particle in the second lowest eigenstate of the well?

2. Relevant equations

3. The attempt at a solution

I have no idea what to do this for this since the wave function is always described as wavelengths in the well, but since its uniform for a/4<x<3a/4 I don't know how to set it up right

2. Oct 24, 2009

### gabbagabbahey

Hi zoso335, welcome to PF!

What do you mean by "the wavefunction is always described by wavelengths in the well"?

3. Oct 25, 2009

### zoso335

well the probability density is the magnitude square of the wave function. And, the wave function of an infinite well always fits an integer multiple of half wavelengths. So, since the probability density is uniform, the wave function has to be uniform in this region, but I don't know how to find the wave function outside this region but still within the well.

4. Oct 25, 2009

### gabbagabbahey

No, the eigenfunctions always fit an integer multiple of half-wavelengths....What are these eigenfunctions? Is it possible for the wavefunction of this particle to be in one of these eigenfunctions? Does it have to be?